In [ ]:
# ----------- Step 1a: Define and categorize the problem statement --------------
# The problem statement is to "Predict the daily bike rental count based on the environmental and seasonal settings"
# This is clearly a 'Supervised machine learning regression problem' to predict a number based on the input features.
# ----------- Step 1a ends here -----------------
In [1]:
# ----------Step 1b: Import all the required libraries ----------
#---- for data transformations----
#install.packages("lubridate")
library(lubridate)
#---- for EDA Visualizations ------
#install.packages("corrplot")
library(corrplot)
#install.packages("ggplot2")
library(ggplot2)
#install.packages("GGally")
library(GGally)
#install.packages("ggExtra")
library(ggExtra)
#---- for model building----
library(caret)
#install.packages("Metrics")
library(Metrics)
#install.packages("randomForest")
library(randomForest)
#install.packages(gbm)
library (gbm)
# ------------------- Step 1b ends here --------------------------
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# ------------------- Step 2: Gather the data -----------------
# Data is provided as .csv file and already split into Test and Train.
# The training set is comprised of the first 19 days of each month, while the test set is the 20th to the end of the month.
# Let's import the data
bike= read.csv("/Users/snehashrungarpawar/Documents/Master in Data Science/DPA/Project/Data/train.csv", header=TRUE)
bike_test = read.csv("/Users/snehashrungarpawar/Documents/Master in Data Science/DPA/Project/Data/test.csv", header=TRUE)
# ------------------- Step 2 ends here --------------------------
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# ------------------- Step 3: Data Preparation ---------------------
# 3a. Analyze Attributes: Check properties of data
# 3b. Complete Data Perform missing value analysis and Impute if needed
# 3c. Correct Data: Check for any invalid data points
# 3d. Create Derived Attributes - Feature Extraction
# 3e. Convert - Converting data to proper formats
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# 3a. Analyze Attributes: Check properties of data
dim(bike)
str(bike)
head(bike, 10)
# 3a -> Inference:
#i. The dataset has 10,886 observations (n=10886) and 12 columns of type int, num and factor.
#ii. Season, Holiday, Working day and weather are categorical variables.
#ii. temp, atemp, humidity, windspeed, casual, registered and count are continuous numerical variables.
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# 3b. Complete Data Perform missing value analysis and Impute if needed
table(is.na(bike))
# 3b -> Inference: There are no null values in the dataset. If it had, then either the rows/columns had to be
# dropped or the null values be imputed based on the % of null values
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# 3c. Correct Data: Check for any invalid data points
# From above observations data doesnot seem to have any invalid datatypes to be handled.
# Let's check for the outliers in EDA step
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# 3d. Create Derived Attributes - Feature Extraction
# Lets extract 'date','month','weekday' and 'year' from 'datetime' column as we will be needing it for analysis
bike$date=as.factor(day(bike$datetime))
bike$year = as.factor(year(bike$datetime))
bike$month = as.factor(month(bike$datetime))
bike$hour = as.factor(hour(bike$datetime))
bike$wkday = as.factor(wday(bike$datetime))
bike_test$date=as.factor(day(bike_test$datetime))
bike_test$year = as.factor(year(bike_test$datetime))
bike_test$month = as.factor(month(bike_test$datetime))
bike_test$hour = as.factor(hour(bike_test$datetime))
bike_test$wkday = as.factor(wday(bike_test$datetime))
# Drop datetime as we have extracted all the above needed information from it
bike = bike[-c(1)]
bike_test = bike_test[-c(1)]
head(bike, 5)
head(bike_test, 5)
# 3d -> Inference: There are no null values in the dataset. If it had, then either the rows/columns had to be
#dropped or the null values be imputed based on the % of null values.
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# 3e. Convert - Converting data to proper formats
# We can clearly see that "season", "holiday", "workingday" and"weather" are categories rather than continous variable.
# Let's convert them to categories
names = c("season", "holiday", "workingday", "weather")
bike[,names] = lapply(bike[,names], factor)
bike_test[,names] = lapply(bike_test[,names], factor)
str(bike)
str(bike_test)
# ------------------- Step 3: Data Preparation ends here --------------------------
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# ------------- Step 4: Exploratory Data Analysis -----------
# 4a. Outlier Analysis
# 4a(1). Visualize continuos variables
par(mfrow=c(1,5))
boxplot(bike$count, main="Count", col="Gray", border = "black")
boxplot(bike$temp, main="Temperature", col="blue", border = "black")
boxplot(bike$atemp, main="Feels Like Temp", col="purple", border = "black")
boxplot(bike$humidity, main="Humidity", col="green", border = "black")
boxplot(bike$windspeed, main="Windspeed", col="orange", border = "black")
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# 4a(2). Visualize categorical variables wrt target variable
par(mfrow=c(3,4))
ggplot(data = bike, aes(x=season, y=count, fill=as.factor(season))) + geom_boxplot() + labs(title="Season vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=weather, y=count, fill=as.factor(weather))) + geom_boxplot() + labs(title="weather vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=holiday, y=count, fill=as.factor(holiday))) + geom_boxplot() + labs(title="holiday vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=workingday, y=count, fill=as.factor(workingday))) + geom_boxplot() + labs(title="workingday vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=year, y=count, fill=as.factor(year))) + geom_boxplot() + labs(title="year vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=month, y=count, fill=as.factor(month))) + geom_boxplot() + labs(title="month vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=wkday, y=count, fill=as.factor(wkday))) + geom_boxplot() + labs(title="weekday vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=hour, y=count, fill=as.factor(hour))) + geom_boxplot() + labs(title="hour vs Count") + theme(legend.title = element_blank())
ggplot(data = bike, aes(x=date, y=count, fill=as.factor(day(date)))) + geom_boxplot() + labs(title="date vs Count") + theme(legend.title = element_blank())
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# 4b. Correlation Analysis
# --------------- Explore Continuous Variables----------------
# 4b(1). Explore continous features
# i. Check distribution of target variable
# ii. Explore correlation between independent continuous variables with target variable
# iii. Plot heatmap for correlation matrix (to check for multicolinearity)
# iv. Visualize the relationship among all continuous variables using pairplots
# v. Explore relationship between independent continuous variables and dependent variables using Joint Plot
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# 4b(1) i. Check distribution of target variable
hist(bike$count, col="blue")
plot(bike$count)
# Inference: Target variable "count" is almost normally distributed.
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# 4b(1) ii. Explore correlation between independent continuous variables with target variable
plot(bike$temp,bike$count)
plot(bike$atemp,bike$count)
plot(bike$windspeed,bike$count)
plot(bike$humidity,bike$count)
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# 4b(1) iii. Plot heatmap for correlation matrix (to check for multicolinearity)
corr <- as.data.frame(lapply(bike[c(5:8, 11)], as.numeric))
corrplot(cor(corr), method = "color", type='lower')
# Inference:
# i. temp and atemp are highly correlated, we would need to drop one of them to remove multicolinearity.
# ii. We can also drop Registered and Casual from our analysis as Counts are categorized as Registered and Casual
# and we will be predicting "Count" variable only.
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# 4b(1) iv. Visualize the relationship among all continuous variables using pairplots
ggpairs(bike[c(5:8)], lower=list(continuous=wrap("smooth", colour="orange")) )
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# 4b(1) v. Explore relationship between independent continuous variables and dependent variables using Joint Plot
# 1. temp vs Count
plot_center = ggplot(bike, aes(x=temp,y=count)) + geom_point(colour="blue") + geom_smooth(method="lm", colour="grey")
ggMarginal(plot_center, type="densigram", colour="blue")
# Inference: temp has good correlation with count.
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# 4b(1).v.2. atemp vs Count
plot_center = ggplot(bike, aes(x=atemp,y=count)) + geom_point(colour="red") + geom_smooth(method="lm", colour="grey")
ggMarginal(plot_center, type="densigram", colour="red")
# Inference: atemp has good correlation with count.
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# 4b(1).v.3. humidity vs Count
plot_center = ggplot(bike, aes(x=humidity,y=count)) + geom_point(colour="green") + geom_smooth(method="lm") + geom_smooth(method="lm", colour="grey")
ggMarginal(plot_center, type="densigram", colour="green")
# Inference: Humidity has low correlation with count.
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# 4b(1).v.4. windspeed vs Count
plot_center = ggplot(bike, aes(x=windspeed,y=count)) + geom_point(colour="orange") + geom_smooth(method="lm", colour="grey")
ggMarginal(plot_center, type="densigram", colour="orange")
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# 4b(1) Inferences Summary - Analysis of continous variables
# 1. Target variable 'count' is almost normally distributed.
# 2. From correlation with dependent variable "count", we can see that 'casual','registered' are very
# highly correlated to cnt. Needs to be dropped from the dataset.
# 3. 'humidity' has low correlation with 'count'. For now, lets keep it.
# 4. atemp and temp has good correlation with 'count'
# 5. From heatmap, we can see that atemp and temp are highly correlated. So we need to drop 1 to remove multicollinearity.
# 6. Since, as seen from jointplot, p(atemp) < p(temp), we can drop 'temp' and retain 'atemp' in the dataset.
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# --------------- Explore Catogorical Variables----------------
# 4b(2) Explore categorical features
# i. Check distribution of categorical variables
ggplot(bike, aes(x=" ",fill=year))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "year")+theme_void()
ggplot(bike, aes(x=" ",fill=month))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "month")+theme_void()
bike$season = factor(bike$season)
ggplot(bike, aes(x=" ",fill=season))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "Season")+theme_void()
bike$holiday = factor(bike$holiday)
ggplot(bike, aes(x=" ",fill=holiday))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "holiday")+theme_void()
ggplot(bike, aes(x=" ",fill=wkday))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "weekday")+theme_void()
bike$workingday = factor(bike$workingday)
ggplot(bike, aes(x=" ",fill=workingday))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "workingday")+theme_void()
bike$weather = factor(bike$weather)
ggplot(bike, aes(x=" ",fill=weather))+ geom_bar(width = 1)+ coord_polar("y")+labs(title = "weather")+theme_void()
In [19]:
# ii. Check how individual categorical features affects the target variable
ggplot(bike, aes(x=season, y=count, fill=year)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) + labs(title="Histogram for Seasons") + labs(x="Season", y="Count")
ggplot(bike, aes(x=year, y=count, fill=year)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) +
labs(title="Histogram for year") + labs(x="year", y="Count")
ggplot(bike, aes(x=month, y=count, fill=month)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) +
labs(title="Histogram for month") + labs(x="month", y="Count")
ggplot(bike, aes(x=holiday, y=count, fill=holiday)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) + labs(title="Histogram for holiday") +labs(x="holiday", y="Count")
ggplot(bike, aes(x=wkday, y=count, fill=wkday)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) + labs(title="Histogram for weekday") +labs(x="weekday", y="Count")
ggplot(bike, aes(x=workingday, y=count, fill=workingday)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) + labs(title="Histogram for working day") +labs(x="working day", y="Count")
ggplot(bike, aes(x=weather, y=count, fill=weather)) +
stat_summary(
fun.y=median,
geom='bar',
position=position_dodge(),
) + labs(title="Histogram for weather") +labs(x="weather", y="Count")
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# iii. Explore trends over time ---- exploring some more pairplots
ggplot(bike, aes(x=season, y=count, group=year, color=year)) +
stat_summary(
fun.y=mean,
geom='line'
) +
stat_summary(
fun.y=mean,
geom='point'
) +
labs(title="Average Count by Month Across Season") +
labs(x="Season", y="Count")
ggplot(bike, aes(x=bike$hour, y=count, group=season, color=season)) +
stat_summary(
fun.y=mean,
geom='line'
) +
stat_summary(
fun.y=mean,
geom='point'
)+
labs(title="Average Count By Hour Of The Day Across Season") +
labs(x="Hour of the Day", y="Count")
ggplot(bike, aes(x=bike$hour, y=count, group=wkday, color=wkday)) +
stat_summary(
fun.y=mean,
geom='line'
) +
stat_summary(
fun.y=mean,
geom='point'
)+
labs(title="Average Count By Hour Of The Day Across Weekdays") +
labs(x="Hour of the Day", y="Count")
ggplot(bike, aes(x=bike$day, y=count, group=day, color=day)) +
stat_summary(
fun.y=mean,
geom='line'
) +
stat_summary(
fun.y=mean,
geom='point'
)+
labs(title="Average Count By Day") +
labs(x="HDay", y="Count")
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# 4c. Drop some variables from the dataset based on the analysis so far
# drop temp, casual, registered and date
bike_subset = bike[-c(5,9:10, 12)]
head(bike_subset,5)
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#------ Step 4: Exploratory Data Analysis ENDS Here------------------
# Final observations:
#1.) 'atemp' and 'temp' are very strongly correlated . Drop 'atemp' from the dataset (since it has higher p-value
#than 'temp')
#2.) 'date' does not seem to have any affect on count of bikes, it can be dropped from the dataset
#------------------------------------------------------------
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#----------Part 5 : Model Builing starts here ----------------------
# 5a. Split data into test and train set
# 5b. Linear Regression
# 5c. Random Forest
# 5d. Gradient Boosting
In [22]:
# 5a. Split data into test and train set
sample_size = floor(0.8 * nrow(bike))
set.seed(1)
train_index = sample(nrow(bike), size = sample_size)
train <- bike[train_index, ]
test <- bike[-train_index, ]
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# 5b. Linear Regression
# Fit Linear Model
# drop atemp, registered, casual and date
train_subset = train[-c(6,9:10, 12)]
test_subset = test[-c(6,9:10, 12)]
lm_fit = lm(count ~ ., data = train_subset)
summary(lm_fit)
# Choosing the best model by AIC in a Stepwise Algorithm
# The step() function iteratively removes insignificant features from the model.
step(lm_fit)
summary(lm_fit)
# Calculate Train RMSLE
y_act_train <- abs(train_subset$count)
y_pred_train <- abs(predict(lm_fit, train_subset))
lm_train_RMSLE = rmsle(y_act_train, y_pred_train)
# Calculate Test RMSLE
y_act_test <- abs(test_subset$count)
y_pred_test <- abs(predict(lm_fit, test_subset))
lm_test_RMSLE = rmsle(y_act_test, y_pred_test)
# Save the results
lm_results = predict(lm_fit, bike_test)
hist(lm_results)
In [24]:
plot(lm_fit)
In [25]:
mse(y_act_train,y_pred_train)
rmse(y_act_train,y_pred_train)
rmsle(y_act_train,y_pred_train)
mse(y_act_test,y_pred_test)
rmse(y_act_test,y_pred_test)
rmsle(y_act_test,y_pred_test)
In [26]:
# 5b. Random Forest
Ntree=500
Mtry = 5
myImportance = TRUE
# Predict Casual Counts
set.seed(1)
CasualData <- subset(train, select = -c(count, registered, date, atemp))
CasualFit <- randomForest(casual ~ ., data=CasualData, ntree=Ntree, mtry=Mtry,
importance=myImportance)
# Predict Registered Counts
RegisteredData <- subset(train, select = -c(count, casual, date, atemp))
RegisteredFit <- randomForest(registered ~ ., data=RegisteredData, ntree=Ntree, mtry=Mtry,
importance=myImportance)
In [34]:
varImpPlot(CasualFit)
varImp(CasualFit)
varImpPlot(RegisteredFit)
varImp(RegisteredFit)
#Inference - Casual Fit: season, holiday, windspeed and weather are not much significant here.
#Inference - Registered Fit: season, holiday, windspeed and weekday are not much significant here.
In [35]:
casualFitFinal <- randomForest(casual ~ hour + year + humidity + month + temp + workingday + wkday,
data=CasualData, ntree=Ntree, mtry=Mtry,importance=myImportance)
RegisteredFitFinal <- randomForest(registered ~ hour + year + month + weather + workingday + humidity + temp,
data=RegisteredData, ntree=Ntree, mtry=Mtry,importance=myImportance)
In [36]:
# Prediction on train data
# Prediction on train data - casual users
PredTrainCasual = round(predict(CasualFit, train),0)
PredTrainCasualFinal = round(predict(casualFitFinal, train),0)
# Prediction on train data - Registered users
PredTrainRegistered = round(predict(RegisteredFit, train),0)
PredTrainRegisteredFinal = round(predict(RegisteredFitFinal, train),0)
# Sum up Casual and Registered to get Total Count
PredTrainCount = PredTrainCasual+PredTrainRegistered
PredTrainCountFinal = PredTrainCasualFinal+PredTrainRegisteredFinal
# Calculate Train RMSLE
rf_train_rmsle_full = rmsle(train$count, PredTrainCount)
rf_train_rmsle2_reduced = rmsle(train$count, PredTrainCountFinal)
# Prediction on test data
# Prediction on test data - casual users
PredTestCasual = round(predict(CasualFit, test),0)
PredTestCasualFinal = round(predict(casualFitFinal, test),0)
# Prediction on test data - registered users
PredTestRegistered = round(predict(RegisteredFit, test),0)
PredTestRegisteredFinal = round(predict(RegisteredFitFinal, test),0)
# Sum up Casual and Registered to get Total Count
PredTestCount = PredTestCasual+PredTestRegistered
PredTestCountFinal = PredTestCasualFinal+PredTestRegisteredFinal
# Calculate Train RMSLE
rf_test_rmsle_full = rmsle(test$count, PredTestCount)
rf_test_rmsle2_reduced = rmsle(test$count, PredTestCountFinal)
In [37]:
cat("Training RMSLE - Linear Regression: ", lm_train_RMSLE)
cat("\nTraining RMSLE - Random Forest (Full Model): ", rf_train_rmsle_full)
cat("\nTraining RMSLE - Random Forest (Reduced Model): : ", rf_train_rmsle2_reduced)
cat("\n\nTest RMSLE - Linear Regression: ", lm_test_RMSLE)
cat("\nTest RMSLE - Random Forest (Full Model): ", rf_test_rmsle_full)
cat("\nTest RMSLE - Random Forest (Reduced Model): ", rf_test_rmsle2_reduced)
In [38]:
hist(bike$count, main="Training Data")
hist(lm_results, main="Linear Regression Fit")
hist(rf_results, main="Random Forest Fit")
# Inference: The distribution of predicted count looks similar to that of train data.
In [39]:
# Save the RF results
rf_test_casual = round(predict(casualFitFinal, bike_test),0)
rf_test_registered = round(predict(RegisteredFitFinal, bike_test),)
rf_results = rf_test_casual + rf_test_registered
In [40]:
gbmtree=4000
iDepth = 3
set.seed(1)
# Predict Casual Counts
CasualData <- subset(train, select = -c(count, registered, atemp, date))
gbm.Casual <- gbm(log1p(casual)~.,data=CasualData,distribution= "gaussian",n.trees=gbmtree,interaction.depth=iDepth)
# Predict Registered Counts
RegisteredData <- subset(train, select = -c(count, casual, atemp, date))
gbm.Registered <- gbm(log1p(registered)~.,data=RegisteredData,distribution= "gaussian",n.trees=gbmtree,interaction.depth=iDepth)
In [41]:
summary(gbm.Casual)
summary(gbm.Registered)
##Inference - gbm Casual: season, holiday, year, windspeed are not much significant here.
##Inference - gbm Registered: holiday, windspeed, season, weather are not much significant here.
In [42]:
gbm.CasualFinal <- gbm(log1p(casual) ~ hour + workingday + temp + month + wkday + humidity + weather,
data=CasualData, distribution= "gaussian",n.trees=gbmtree,interaction.depth=iDepth)
gbm.RegisteredFinal <- gbm(log1p(registered) ~ hour + year + workingday + month + wkday + humidity + temp,
data=RegisteredData, distribution= "gaussian",n.trees=gbmtree,interaction.depth=iDepth)
In [43]:
# Prediction on train data
# Prediction on train data - casual users
gbm.PredTrainCasual <- predict(gbm.Casual, train, n.trees=gbmtree)
gbm.PredTrainCasualFinal <- predict(gbm.CasualFinal, train, n.trees=gbmtree)
# Prediction on train data - Registered users
gbm.PredTrainRegistered <- predict(gbm.Registered, train, n.trees=gbmtree)
gbm.PredTrainRegisteredFinal <- predict(gbm.RegisteredFinal, train, n.trees=gbmtree)
# Sum up Casual and Registered to get Total Count
gbm.PredTrainCount <- round(exp(gbm.PredTrainCasual) - 1, 0) + round(exp(gbm.PredTrainRegistered) - 1, 0)
gbm.PredTrainCountFinal <- round(exp(gbm.PredTrainCasualFinal) - 1, 0) + round(exp(gbm.PredTrainRegisteredFinal) - 1, 0)
# Calculate Train RMSLE
gbm.rf_train_rmsle_full <- rmsle(train$count, gbm.PredTrainCount)
gbm.rf_train_rmsle2_reduced <- rmsle(train$count, gbm.PredTrainCountFinal)
# Prediction on test data
# Prediction on test data - casual users
gbm.PredTestCasual = predict(gbm.Casual, test, n.trees=gbmtree)
gbm.PredTestCasualFinal = predict(gbm.CasualFinal, test, n.trees=gbmtree)
# Prediction on test data - registered users
gbm.PredTestRegistered = predict(gbm.Registered, test, n.trees=gbmtree)
gbm.PredTestRegisteredFinal = predict(gbm.RegisteredFinal, test, n.trees=gbmtree)
# Sum up Casual and Registered to get Total Count
gbm.PredTestCount = round(exp(gbm.PredTestCasual) - 1, 0) + round(exp(gbm.PredTestRegistered) - 1, 0)
gbm.PredTestCountFinal = round(exp(gbm.PredTestCasualFinal) - 1, 0) + round(exp(gbm.PredTestRegisteredFinal) - 1, 0)
# Calculate Test RMSLE
gbm.rf_test_rmsle_full = rmsle(test$count, gbm.PredTestCount)
gbm.rf_test_rmsle2_reduced = rmsle(test$count, gbm.PredTestCountFinal)
In [44]:
gbm.rf_train_rmsle_full
gbm.rf_train_rmsle2_reduced
gbm.rf_test_rmsle_full
gbm.rf_test_rmsle2_reduced
In [46]:
par(mfrow=c(3,2))
plot(y_act_train, y_pred_train, main="Linear Regression - Train Dataset", xlab="actual", ylab="predicted")
plot(y_act_test, y_pred_test, main="Linear Regression - Test Dataset", xlab="actual", ylab="predicted")
plot(train$count, PredTrainCount, main="Random Forest - Train Dataset", xlab="actual", ylab="predicted")
plot(test$count, PredTestCount, main="Random Forest - Test Dataset", xlab="actual", ylab="predicted")
plot(train$count, gbm.PredTrainCountFinal, main="Gradient Boosting - Train Dataset", xlab="actual", ylab="predicted")
plot(test$count, gbm.PredTestCountFinal, main="Gradient Boosting - Test Dataset", xlab="actual", ylab="predicted")
In [48]:
cor(y_act_train, y_pred_train)
cor(y_act_test, y_pred_test)
cor(train$count, PredTrainCountFinal)
cor(test$count, PredTestCountFinal)
cor(train$count, gbm.PredTrainCountFinal)
cor(test$count, gbm.PredTestCountFinal)
In [49]:
par(mfrow=c(2,2))
plot(test_subset$count, main = "Linear Model", ylab = "Test Set Rental Count", pch = 20)
points(predict(lm_fit, newdata = test), col = "red", pch = 20)
plot(test_subset$count, main = "Random Forest", ylab = "Test Set Rental Count", pch = 20)
points(PredTestCountFinal, col = "red", pch = 20)
plot(test_subset$count, main = "Gradient Boosting", ylab = "Test Set Rental Count", pch = 20)
points(gbm.PredTestCountFinal, col = "red", pch = 20)
In [50]:
# Save the RF results
gbm_test_casual = round(predict(gbm.CasualFinal, bike_test, n.trees=gbmtree),0)
gbm_test_registered = round(predict(gbm.RegisteredFinal, bike_test, n.trees=gbmtree),0)
gbm_results = gbm_test_casual + gbm_test_registered
In [51]:
par(mfrow=c(2,2))
hist(bike$count, main="Training Data")
hist(lm_results, main="Linear Regression Fit")
hist(rf_results, main="Random Forest Fit")
hist(rf_results, main="Gradient Boosting Fit")
In [52]:
par(mfrow=c(2,2))
hist(bike$count, main="Training Data")
hist(lm_results, main="Linear Regression Fit")
hist(rf_results, main="Random Forest Fit")
hist(rf_results, main="Gradient Boosting Fit")
In [ ]: